Obamacare is supposed to be a 21st-century shopping experience, but the health law can’t escape living in an older paper world.

One of President Barack Obama’s favorite claims about his health law is that finding coverage is as easy as going online to buy a plane ticket. That’s always been an overstatement, even before the online insurance marketplaces’ glitch-filled launch.

“I think the goal has always been to drive as many people as possible online, but who knows?” said Shelby Gonzales, a senior health policy analyst for the left-leaning Center on Budget and Policy Priorities. “People have always been doing paper applications for a long time, so it’s hard to know.”

The whole appeal of shopping for coverage online is that a person ideally could do everything in one sitting: determine eligibility for Medicaid, CHIP or premium tax credits, and then sift through health plans, compare and choose. Another major benefit is that the online system should instantly flag application errors that would take longer to catch on paper.

Tricia Brooks, a senior fellow at Georgetown’s Center for Children and Families, said the application for exchange coverage is already more complicated than Medicaid and CHIP for two major reasons: Subsidy eligibility is checked against tax filings and whether a potential enrollee already has affordable coverage through work.

“I just hope that we have extremely few paper applications coming through,” Brooks said. “They aren’t an effective way to do this. They certainly are going to be more administratively cumbersome because someone is going to have to sit down and input this data.”

The Obama administration has been prepared for a crush of paper. Over the summer, it awarded a $1.2 billion contract to Serco, which says it expects to process 6.2 million paper applications in the health law’s first open enrollment period running through the end of March.

As the exchange websites have been plagued with long wait times, temporary shutdowns and error messages since opening Oct. 1, some early shoppers have recently decided to ditch the Web in favor of paper applications.

“We see some navigators that have pushed the paper applications,” said Anne Filipic, president of Enroll America, referring to in-person assistance funded by the law to educate consumers about their coverage options. Those navigators, she said, can still help people compare health plans — something that consumers locked out of HealthCare.gov this week haven’t been able to do.

“Navigators have access through [the Centers for Medicare & Medicaid Services and] the ability to really compare those plans, walk someone through the process, for them to be able to get the information,” Filipic said on a Thursday call with reporters.

Consumers have other options. The feds and each state-run exchange have opened call centers, agents and brokers have been certified to sell exchange plans, and thousands of stores — like major retail pharmacy and tax preparation firms — are offering on-site help.

Kevin Counihan, CEO of Connecticut’s exchange, has made it a mission to abolish paper applications — as much as possible, anyway. The Connecticut exchange, known as Access Health CT, doesn’t offer a fax number and is urging stakeholders to just say no to paper.

“We are actively discouraging paper to the point where we’re going to run it as part of our advertising campaign,” Counihan said in a recent interview. “Paper, to us, is not the optimal customer experience. It’s clunky, and it’s subject to error.” While Connecticut’s exchange early on faced glitches and delays similar to other states, it was open for business and enrolling customers on the first day.